Wednesday, September 4, 2013

The design of a decentralized currency (part 2)

Last time, we learned that currency, in its purest form, is simply an accounting device to enforce a cooperative tit-for-tat system of exchange. If Alice provides something of value to Bob, she obtains a token enabling her to acquire something of comparable value from Bob or any other participant in the currency. In principle, we could execute these same mutually beneficial transactions using explicit contracts, except that would be rather inconvenient. Thus, according to this view, "so long as we all agree", it is in some sense arbitrary what tokens we use for trade--it could be seashells, shiny discs of yellow metal, scraps of paper, or 100 digit numbers. That is, there is no "one true" token type to use as a medium of exchange, we merely prefer one sort of token over another for properties like convenience, stability, and so on.

This view, of money as purely an accounting device ("medium of exchange" is a term often used) differs from how people have thought of money for most of human history. For most of human history, money has been tied to some widely valued commodity, often gold and/or silver, with each unit of currency corresponding to some amount of this commodity (often literally, via use of gold coins with some fixed weight, or via more convenient paper notes which banks agree to exchange for actual gold on demand). Commodity-backed currencies tend to arise naturally, without any coordination or central government.

But our goal here is developing a pure currency, a currency which is only the accounting device, not one tied to any commodity that is valued for its own sake (we'll see in a later post that there are problems with commodity-backed currencies). There are difficulties with driving adoption of a pure currency (the usual solution is for a government to mandate its use and generate 'artificial' demand for it by forcing citizens to pay taxes in the currency) and preserving its stability that we'll discuss later. But a pure currency gets at the essence of what money helps people achieve--conduct mutually beneficial transactions with a minimum of transaction costs.

If we view currency as merely an accounting device for this cooperative system, a question arises: why is there so much complexity around our monetary system? Why not simply allocate a fixed number of units of currency (which could all be assigned meaningless 100-digit numbers) and "just get everyone to agree" (or have government force!) use of these tokens as a medium of exchange? To see why this and other related systems like BitCoin are unsuitable, we need to examine the critical role of interest in a monetary system and understand what factors ought to affect the rate of interest.

Interest is broadly defined as compensation for any contract whose payout(s) occur in the future. For instance, when you obtain a loan to purchase a house, the bank charges interest as compensation for an (uncertain) stream of future monthly payments. The same principle, of compensation for future payouts, is at work in all manner of mutually beneficial contracts.

In this post, are are going to try to get to the bottom of why a future payout (as opposed to a present payout) warrants additional compentation. Intuitively, it seems natural this should be so, but we want to be very careful to separate out what factors are at work here. As we'll see, there is one fundamental factor with serious consequences for any monetary system.

What factors affect interest rates?

Let us start by pondering a simple thought experiment. Suppose Alice is a neighbor of yours. She knocks on your door one day and asks to borrow your laptop... for a full year. At the end of the year, she tells you, she'll agree to return your laptop or another laptop of the same model and condition (let's pretend that all your personal data is stored in the cloud, so you don't care if you get back your exact laptop). Alice has a contract all written up and ready for you to sign. She asks you: what do you expect in compensation for agreeing to this contract?

You might request anything as compensation for this (uncertain) future payout: $50 now, at contract signing, or a stream of payments of $5 per month. Or you might demand a 25% 'better' laptop after one year, or a cappuccino delivered to your door every Thursday for six months. What's important here is not what you ultimately decide to request, but what factors affect your request. Before continuing on, you may want to stop and think about this question.

Here are some possible answers. We'll deconstruct them in a minute:

  • As with any contract, a general concern is that you can't really be sure the other party (Alice) will hold up their end of the bargain. Yes, Alice is your neighbor and seems trustworthy, but anything could happen. What if she just skips town? Or sells your laptop to feed a secret cocaine habit then refuses (or is unable) to provide you with a comparable laptop a year from now? We say there is some risk of default, the chance that the person you are loaning to may be unable to pay back the loan. (Or more generally, counterparty risk, the risk that the other party to the contract, Alice, may not be willing or able to uphold their obligations) To offset this risk, you require some compensation.
  • As with any market, the buyer must pay enough to bid the good or service away from its possible alternative uses. During the time Alice is using your laptop, you are obviously not using it. The laptop provides you with enjoyment and utility, and this contract Alice is proposing asks you to put off that enjoyment for a year, purchase a replacement in the meantime, or find other, less convenient ways of doing the same things (using the computer at work, using your iPad instead, etc). For this you expect compensation. Alice must also bid use of the laptop away from others interested in it (for instance, if Tom, Dick, and Harry are all lined up, willing and able to pay $100 to rent your laptop for a year).
  • Lastly, you have some expectation that computer technology will continue advancing, making your computer "worth less" in a year. We can make this argument more precise, but to illustrate the idea, suppose you believe that computers will become 30% better (for "the same" cost) a year from now. Then at the very least, you ought to expect Alice to pay you 30% of the current value of your computer now or provide equivalent compensation, in addition to considering the other factors above. After all, if you didn't price this factor into the contract, Alice could immediately sell your laptop now for (let's just say) $100, then buy a brand new, older model equivalent for $70 one year from now, netting her a $30 profit! Related to this, even if you expect your laptop to be worth the same, there is some uncertainty around this expectation because it is with regard to a future event. If you didn't factor this into the price you negotiate, you are effectively taking on additional risk for no additional compensation.

Now each of these factors are interesting in their own right, but in an effort to get at the essence of the problem, let's idealize our scenario a bit. Suppose that, instead of Alice, you are approached by Trent. For purposes of this thought experiment, let us assume that Trent, who also happens to be your friend, is known worldwide as the most trustworthy person in existence and has zero risk of defaulting on his obligations. If the earth still exists in a year, Trent will provide you with a laptop, no doubt about it. This eliminates any interest you might charge due to factor 1, the risk of default.

Furthermore, since Trent is your friend, suppose you aren't really looking to maximize how much you get from the deal. You only want to ensure that you "break even" and are fine with selling Trent the contract "at cost". Thus, the fact that Tom, Dick, and Harry are all lined up willing to pay $100 is irrelevant. The only thing you have to decide is how much the use of your laptop is worth to you over the one year period, because that is what you will be giving up.

What about factor 3, your expectations (and uncertainty around) economic growth in laptop production. Even if Trent is perfectly trustworthy, and even if you don't mind just breaking even, this does not change your expectation that it will be easier/cheaper to obtain a comparable laptop one year from now. And if it is cheaper to obtain a comparable laptop one year from now, that implies (among other things) that if you wait a year to sell the laptop that Trent wishes to rent, you'll have to sell it for less than you could sell it for now. From this we conclude that that the possibility of economic growth must always be priced into any contract whose payout occurs in the future.

Now consider the related question--suppose that instead of asking for use of your laptop for a year, Trent (or Alice) asks instead for $100, to be paid back in one year. What would you expect as compensation? Notice that the same factors apply to your decision:

  • You expect to be compensated for the possibility that Alice won't pay you back. Perhaps you request $10 now, in addition to the $100 a year from now, to account for this possibility. Or perhaps you request $112 after a year. For Trent, you don't bother with this premium.
  • Even for Trent, you will expect some premium due to the fact that receiving $100 a year from now is not as good as $100 now. This isn't just because you expect the dollar might depreciate by 3% in a year due to inflation, which we'll discuss in the next post; there's just that same opportunity cost of not being able to spend that $100 now on other goods or services you value. After all, with that $100 in your pocket, you could buy those cappuccinos for yourself every Thursday for six months, something that you derive enjoyment from. Lending out your $100 means delaying this enjoyment for a year. We say there is a time preference.
  • Just as it may be easier to obtain a comparable laptop a year from now, it may be easier to obtain $100 one year from now. There are various reasons why this could be so. One possibility is an increase in the money supply or availability of credit, due to actions of the central bank. We are going to ignore this factor, since our goal is a central-bank free currency and we don't want any central authority making decisions which affect interest rates. But the other key factor that may make it easier to obtain $100 a year from now is an increase in the rate at which currency circulates, also known as the velocity of money. We will be talking a lot more about velocity in future posts, but we can see that if on average a dollar changes hands more frequently, that implies dollars are easier to come by.

We are going to focus exclusively on this last factor, not because time preferences are uninteresting, but because this preference is a personal decision. A wealthy individual with more cash than he/she could reasonably spend in the next year may not demand as much interest from a loan due to this factor as someone who needs the cash for some short-term expenditures. Thus, it is somewhat orthogonal--individuals will price this factor into interest rates on loans and other contracts, but the monetary system itself does not need to be aware of these preferences.


We've examined what factors determine interest rates, then narrowed down these factors to a single, fundamental one, which could be summarized in the following way:

Any payout that occurs in the future, in whatever units (be it dollars, laptops, or cappuccinos), must account for the possibility that those units have differing relative value in the future as compared to the present.

In the next post, we are going to reason through how failure to account for this factor in a currency can lead to serious distortion of markets and financial instability. This will make it clear why commodity-backed currencies like a gold standard and simplistic 'fixed' currencies like BitCoin are inadequate and motivate design of 'smart' digital currency that explicitly accounts for changes in monetary velocity. We'll then compare the velocity-adjusted currency we develop to a typical monetary system managed by a central bank.

We've been a bit vague about this concept of "value" so far and what it means for an asset to change in value. This is something we'll delve into further in the next post.


Anonymous said...

I'm curious to see where you're going with this. Nothing you've written so far is unorthodox in terms of classic macroeconomics. And you've hinted that you realize the inadequacy of a purely commodity or fixed stock money.

At the same time, all that seems beside the point of whether you need a central bank. Paper money achieved great prominence in the United States because of a shortage of specie in the thirteen colonies, with no central bank. Up until the National Banking Act of 1863, private banknotes were issued and used as currency throughout the United States, again with no central bank. Finally, the Federal Reserve Bank is the third central bank that the US has enjoyed, after the the First Bank of the United States, and the Second Bank of the United States. Seventy years after the Second Bank was liquidated, the Federal Reserve was chartered, because central banks are intended to solve problems in the real economy.

So I have to say I am looking forward to seeing where you are going.

Paul Chiusano said...

@Anonymous -

If you want to jump ahead to see what kind of thing I'm thinking about, see this question I asked on Quora. I wouldn't get too hung up on the details of that straw man, but that is in the ballpark of what I'm thinking about.

I was hoping to get some actual economists to weigh in but the question hasn't seen much activity. Send me an email if you have any connections.